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Dimensionality Reduction

Dimensionality Reduction

  • Purpose
    • Avoid curse of dimensionality
    • Reduce amount of time and memory required by data mining algorithms
    • Allow data to be more easily visualized
    • May help to eliminate irrelevant features or reduce noise
  • Techniques
    • Principle Component Analysis
    • Singular Value Decomposition
    • Others: supervised and non-linear techniques

Data Dimensionaity

  • From a theoretical point of view, increasing the number of features should lead to better performance
  • In practice, the inclusion of more features leads to worse performance (i.e., curse of dimensionality)
  • The number of training examples required increases exponentially with dimensionality

Curse of Dimensionality

  • When dimensionality increases, data becomes increasingly sparse in the space that it occupies
  • Definitions of density and distance between points, which is critical for clustering and outlier detection, become less meaningful

Dimensionality Reduction

  • Purpose
    • Avoid curse of dimensionality
    • Reduce amount of time and memory required by data mining algorithms
    • Allow data to be more easily visualized
    • May help to eliminate irrelevant features or reduce noise
  • Techniques
    • Principle Component Analysis
    • Single Value Decomposition
    • Others: Supervised and non-linear techniques

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https://www.datacamp.com/community/tutorials/principal-component-analysis-in-python

Feature Subset Selection

  • Another way to reduce dimensionality of data

  • Redundant features

    • duplicate much or all of the information contained in one or more other attributes
    • Example: purchase price of a product and the amount of sales tax paid
  • Irrelevant features

    • contain no information that is useful for the data mining task at hand
    • Examples: students' ID is often irrelevant to the task of predicting students' GPA
  • Evaluate a subset of feature

  • Search for the best subset

Techniques

Brute-force approach

Try all possible feature subsets as input to data mining algorithm

Embedded approaches

Feature selection occurs natually as part of the data mining algorithm

Fiter approaches

Features are selected before data mining algorithm is run

Wrapper approaches

Use the data mining algorithm as a black box to find best subset of attributes

Feature Creation

  • Create new attributes that can capture the important information in a data set much more efficiently than the original attributes
  • Three general methodologies
    • Feature Extraction - domain-specific
    • Mapping data to new space
    • Feature construction - combining features

Introduction to dimensionality reduction - Blog | Hex